Semifields \((S,+,\cdot)\) in the meaning of this article are division rings with identity, where the multiplication is not necessarily associative. The centre of such a semifield is defined as \(K=\{ a\in S\mid (ab)c=a(bc), b(ac)=(ba)c, b(ca)=(bc)a, ab=ba\) for all \(b,c\in S\}\). If \(S\) is a finite semifield then its centre is a finite field \(F_q\). An element \(a\in S\) of a finite semifield of order \(r\) is left primitive if \(S\setminus \{0\} = \{a,a^{(2},\dots , a^{(r-1}\}\), where \(a^{(i}\) is defined recursively by \(a^{(1}=a\) and \(a^{(i+1} = aa^{i}\). The semifield \(S\) is called left primitive if it contains a left primitive element. Right primitive semifields are defined dually. The main result is: Let \(S\) be a semifield which is \(n\)-dimensional over its centre \(F_q\). For \(n=3\) and any \(q\), \(S\) is left and right primitive. This is also true if \(n\) is prime and \(q\) satisfies \(q^{n-1} > (n-1)(n-2)q^{n-{3 \over 2}} + 5n^{13\over 3}q^{n-2} + 1\). This result is obtained by showing that the associated polynom of \(S\) is a norm form in that cases.